Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Mahatab, Kamalakshya"'
Autor:
Chirre, Andrés, Mahatab, Kamalakshya
Let $S(\sigma,t)=\frac{1}{\pi}\arg\zeta(\sigma+it)$ be the argument of the Riemann zeta-function at the point $\sigma+it$ in the critical strip. For $n\geq 1$ and $t>0$, we define \begin{equation*} S_{n}(\sigma,t) = \int_0^t S_{n-1}(\sigma,\tau) \,d\
Externí odkaz:
http://arxiv.org/abs/2006.04288
We consider $L$-functions $L_1,\ldots,L_k$ from the Selberg class which have polynomial Euler product and satisfy Selberg's orthonormality condition. We show that on every vertical line $s=\sigma+it$ with $\sigma\in(1/2,1)$, these $L$-functions simul
Externí odkaz:
http://arxiv.org/abs/2001.09274
Autor:
Chirre, Andrés, Mahatab, Kamalakshya
Let $S(t)$ denote the argument of the Riemann zeta-function, defined as $$ S(t)=\dfrac{1}{\pi}\,\Im\log\zeta(1/2+it). $$ Assuming the Riemann hypothesis, we prove that $$ S(t)=\Omega_{\pm}\bigg(\dfrac{\log t\log\log\log t}{\log\log t}\bigg). $$ This
Externí odkaz:
http://arxiv.org/abs/1904.11051
Autor:
Dixit, Anup B., Mahatab, Kamalakshya
In this paper, we study lower bounds of a general family of $L$-functions on the $1$-line. More precisely, we show that for any $F(s)$ in this family, there exists arbitrary large $t$ such that $F(1+it)\geq e^{\gamma_F} (\log_2 t + \log_3 t)^m + O(1)
Externí odkaz:
http://arxiv.org/abs/1901.01625
Autor:
Mahatab, Kamalakshya
We estimate the number of composite elements in the $n$-th grade of the group semiring of finite boolean groups. In view of this result we may conjecture that the composites in the semiring of finite groups are thinly dispersed.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/1808.02331
For a fixed $\theta\neq 0$, we define the twisted divisor function $$ \tau(n, \theta):=\sum_{d\mid n}d^{i\theta}\ .$$ In this article we consider the error term $\Delta(x)$ in the following asymptotic formula $$ \sum_{n\leq x}^*|\tau(n, \theta)|^2=\o
Externí odkaz:
http://arxiv.org/abs/1807.10047
Autor:
Mahatab, Kamalakshya
Let $Z(t):=\zeta\left(\frac{1}{2}+it\right)\chi^{-\frac{1}{2}}\left(\frac{1}{2}+it\right)$ be Hardy's function, where the Riemann zeta function $\zeta(s)$ has the functional equation $\zeta(s)=\chi(s)\zeta(1-s)$. We prove that for any $\epsilon>0$, \
Externí odkaz:
http://arxiv.org/abs/1807.08554
In recent years a variant of the resonance method was developed which allowed to obtain improved $\Omega$-results for the Riemann zeta function along vertical lines in the critical strip. In the present paper we show how this method can be adapted to
Externí odkaz:
http://arxiv.org/abs/1803.00760
Autor:
Mahatab, Kamalakshya
We prove that for the Steinhaus Random Variable $z(n)$ \[\mathbb{E}\left(\left|\sum_{n\in E_{N, m}}z(n)\right|^6\right)\asymp |E_{N, m}|^3 \text{ for } m\ll(\log\log N)^{\frac{1}{3}},\] where \[E_{N, m}:=\{1\leq n:\Omega(n)=m\}\] and $\Omega(n)$ deno
Externí odkaz:
http://arxiv.org/abs/1710.08201
We prove that there are arbitrarily large values of $t$ such that $|\zeta(1+it)| \geq e^{\gamma} (\log_2 t + \log_3 t) + \mathcal{O}(1)$. This essentially matches the prediction for the optimal lower bound in a conjecture of Granville and Soundararaj
Externí odkaz:
http://arxiv.org/abs/1703.08315